Besides, higher capital requirements "may have an unintended effect of enabling banks to take more tail risk without the fear of breaching the minimal capital ratio in non-tail risky project realizations."

Excerpts of the paper's introduction:

Regulatory reform in the wake of the recent financial crisis has focused on an increase in capital cushions of financial intermediaries. Basel III rules have doubled the minimal capital ratio, and directed banks to hold excess capital as conservation and countercyclical buffers above the minimum (BIS, 2010). These arrangements complement traditional moral suasion and individual targets used by regulators to ensure adequate capital cushions.

There are two key arguments in favor of higher capital. The first is an ex post argument: capital can be seen as a buffer that absorbs losses and hence reduces the risk of insolvency. This risk absorption role also mitigates systemic risk factors, such as collective uncertainty over counterparty risk, which had a devastating propagation effect during the recent crisis. The second considers the ex ante effects of buffers: capital reduces limited liability-driven incentives of bank shareholders to take excessive risk, by increasing their “skin in the game” (potential loss in case of bank failure; Jensen and Meckling 1976, Holmstrom and Tirole 1997).

Yet some recent experience calls for caution. First, banks are increasingly exposed to tail risk, which causes losses only rarely, but when those materialize they often exceed any plausible initial capital. Such risks can result from a number of strategies. A first example are carry trades reliant on short term wholesale funding, which in 2007-2008 produced highly correlated distressed sales (Gorton, 2010). A second example is the reckless underwriting of contingent liabilities on systemic risk, callable at times of collective distress (Acharya and Richardson, 2009). Finally, the combination of higher profits in normal times and massive losses occasionally arises in undiversified industry exposures to infl ated housing markets (Shin, 2009). A useful review of such strategies is provided in Acharya et al. (2009); IMF (2010) highlights the importance of recognizing tail risk in financial stability analysis. Since under tail risk banks do not internalize losses independently of the level of initial capital, the buffer and incentive effects of capital diminish. Higher capital may become a less effective way of controlling bank risk.

Second, a number of major banks, particularly in the United States, appeared highly capitalized just a couple of years prior to the crisis. Yet these very intermediaries took excessive risks (often tail risk, or highly negatively skewed gambles). In fact, anecdotal evidence suggests that highly capitalized banks were looking for ways to put at risk their capital in order to produce returns for shareholders (Berger et al. 2008, Huang and Ratnovski 2009). Therefore, higher capital may create incentives for risk-taking instead of mitigating them.

This paper seeks to study these concerns by reviewing the effectiveness of capital regulation, and in particular of excess capital buffers (that is, above minimum ratios), in dealing with tail risk events. We reach two key results.

First, we show that the traditional buffer and incentives effects of capital become less powerful when banks have access to tail risk projects. The reason is that tail risk realizations can wipe out almost any level of capital. Left tails limit the effectiveness of capital as the absorbing buffer and restrict “skin in the game” because a part of the losses is never borne by shareholders. Hence, under tail risk, excess risk-shifting incentives of bank shareholders may exist almost independently of the level of initial or required capital.

Second, having established that under tail risk the benefits of higher capital are limited, we consider its possible unintended effects. We note that capital regulation also affects bank risk choices through the threat of capital adjustment costs when banks have to raise equity to comply with minimum capital ratios. (These costs are most commonly associated with equity dilution under asymmetric information on the value of illiquid bank assets,Myers and Majluf, 1984, or reduced managerial incentives for efficiency, Jensen, 1986).2 Similar to "skin in the game", capital adjustment costs make banks averse to risk, and may discourage risky bank strategies. However, unlike "skin in the game", the incentive effects of capital adjustment costs fall with higher bank capital because the probability of breaching the minimal capital ratio decreases.

Of course, if highly capitalized banks internalized all losses, they would have taken risk only if that was socially optimal (would have offered a higher NPV). Yet this result changes dramatically once we introduce tail risk. Then, even banks with high capital never internalize all losses, and may take excess risk. Moreover, the relationship between capital and risk can become non-monotonic. The reason is interesting. In the first place, tail risk leads to insolvency whatever the initial bank capital, so higher capital does not sufficiently discourage risk-taking for well capitalized banks through "skin in the game". At the same time, higher excess capital allows banks to take the riskier projects without breaching the minimal capital ratio (and incurring large capital adjustment costs) in the case of low (non tail) returns. So under tail risk, higher capital may create conditions where highly capitalized banks take more excess risk. Further, we show that the negative effect of extra capital on risk-taking becomes stronger when banks get access to projects with even higher tail risk.

To close the model, we derive the bank’s choice of initial capital in the presence of tail risk, and the implications for optimal capital regulation. We show that a bank may choose to hold higher capital in order to create a cushion over the minimal capital requirement so as to be able to take tail risk without the fear of a corrective action in case of marginally negative project realizations. Then, capital regulation has to implement two bounds on the values of bank capital: a bound from below (a minimal capital ratio) to prevent ordinary risk-shifting and a bound from above (realistically, in the form of special attention devoted to banks with particularly high capital) in order to assure that they are not taking tail risk.

These results are interesting to consider in historic context. Most sources of tail risk that we described are related to recent financial innovations. In the past, tail risk in traditional loan-oriented depository banking was low (both project returns and withdrawals largely satisfied the law of large numbers), hence “skin in the game” effects dominated, and extra capital led to lower risk-taking. Yet now, when banks have access to tail risk projects, the buffer and "skin in the game" effects that are the cornerstone of the traditional approach to capital regulation became weak, while effects where higher capital enables risk-taking became stronger. Therefore, due to financial innovation, the beneficial effects of higher capital were reduced, while the scope for undesirable effects increased.

The paper has policy implications relevant for the current debate on strengthening capital regulation. The simpler conclusion is that it is impossible to control all aspects of risk-taking using a single instrument. The problem of capital buffers is that they are effective as long as they can minimize not just the chance of default, but also the loss given default. Contractual innovation in finance has enabled intermediaries to manufacture risk profiles which allow them to take maximum advantage of limited liability even with high levels of capital. The key to contain gambles with skewed returns is to either prohibit extreme bets, or to increase their ex ante cost. Leading policy proposals now emerging are to charge prudential levies on strategies exposed to systemic risk (Acharya et al., 2010), such as extremely mismatched strategies (Perotti and Suarez, 2009, 2010), or derivative positions written on highly correlated risks.

A more intricate conclusion relates to implications for capital regulation. The results do not imply that less capital is better: this was not the case in recent years. However, they suggest the following. First, regulators should acknowledge that traditional capital regulation has limitations in dealing with tail risk. This is similar, for example, to an already-accepted understanding that it has limitations in dealing with correlation risk (Acharya, 2009). Second, banks with significant excess capital may be induced to take excess risk (in order to use or put at risk their capital), as amply demonstrated by the crisis experience. Hence, simply relying on higher and "excess" capital of banks as a means of crisis prevention may have ruinous effects if it produces a false sense of comfort. Finally, authorities should introduce complementary measures to target tail risk next to the policy on pro-cyclical and conservation buffers. In this context, enhanced supervision with a focus on capturing tail risk may be essential.

We see our paper as related to two key strands of the banking literature. First are the papers on the unintended effects of bank capital regulation. Early papers (Kahane 1977, Kim and Santomero 1988, Koehn and Santomero 1980) took a portfolio optimization approach to banking and caution that higher capital requirements can lead to an increase in risk of the risky part of the bank’s portfolio. Later studies focus on incentive effects. Boot and Greenbaum (1993) show that capital requirements can negatively affect asset quality due to a reduction in monitoring incentives. Blum (1999), Caminal and Matutes (2002), Flannery (1989) and Hellman et al. (2000) argue that higher capital can make banks take more risk as they attempt to compensate for the cost of capital. Our paper follows this literature, with a distinct and contemporary focus on tail risk.3 On the empirical front, Angora et al. (2009) and Bichsel and Blum (2004) find a positive correlation between levels of capital and bank risk-taking.

The second strand are the recent papers on the regulatory implications of increased sophistication of financial intermediaries and the recent crisis. These papers generally argue that dealing with new risks (including systemic and tail risk) requires new regulatory tools (Acharya and Yorulmazer 2007, Acharya et al. 2010, Brunnermeier and Pedersen 2008, Huang and Ratnovski 2011, Perotti and Suarez 2009, 2010).